Expression of type Conditional

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, l
from proveit.logic import InSet
from proveit.numbers import Abs, Exp, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Conditional(Exp(Abs(_rel_indexed_alpha), two), InSet(l, _neg_domain))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 30 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 32
4	Literal
5	ExprTuple	27, 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 34 operands: 17
14	Operation	operator: 38 operand: 21
15	Literal
16	ExprTuple	19
17	ExprTuple	20, 40
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 38 operand: 28
21	Operation	operator: 34 operands: 25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	28
25	ExprTuple	29, 40
26	Literal
27	Variable
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal